Convert Polar Coordinates To Rectangular Coordinates: Learn How To Find The Rectangular Coordinates Of A Point In Math.

5π/6 (-√3/2, 1/2)

The polar coordinates of the given point are (1, 5π/6).

To better understand the given point in polar coordinates, let’s first review what each component means.

In polar coordinates, a point is represented by an ordered pair (r, θ) where r is the distance from the origin (also known as the magnitude or modulus) and θ is the angle made with the positive x-axis, also known as the argument or phase angle.

Here, we are given the point (−√3/2, 1/2) in rectangular coordinates and we are required to convert it into polar coordinates. To do so, we can use the following formulas:

r = √(x² + y²)
θ = atan(y/x)

where x is the horizontal component and y is the vertical component.

Substituting the given values, we get:

r = √[(−√3/2)² + (1/2)²] = √(3/4 + 1/4) = √1 = 1
θ = atan(1/2(−√3/2)) = atan(−√3/4)

Now, we need to find the precise angle in radians that satisfies the given condition (5π/6). Since we know that θ is in standard position (on the x-axis), and the point is in the second quadrant (y-coordinate is positive), we can use the reference angle (π/6) and subtract it from π to get the actual angle.

θ = π – π/6 = 5π/6

Therefore, the polar coordinates of the given point are (1, 5π/6).

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